How do I properly use core matte to keep green section of shirt on using green screen keying?
Hard to tell without seeing your setup, but my guess is :  the mask plugged in Core Matte always output a 100% value, while the rest of the shirt output a lower value ; ie, there is some green in the shirt and the keying node make it a little bit transparent. Nothing noticeable at first, but noticeable by contrast with the mask.

You can verify that by compositing the output of the Keying node on a grid, or on a vivid color. Or plug the Matte output to a Viewer, and make sure there is only black or white areas, no gray. That will make obvious if some areas aren't keyed correctly. If that's the case, adjust the parameters of the keying node.